Please solve this problem

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# Question

# Answer

We can apply the following logic :

1 ) When the distance travelled by 2 objects is the same, the ratio in terms of time taken will be the **opposite** of the ratio in terms of speed

2) When the time taken is the same, the ratio in terms of speed will be the **same** as the ratio in terms of distance travelled

The first clue is “Winnie drove 8 hours from City P to City Q while Suming took 14 hours to travel from City Q to City P”

Since the distance travelled by Winnie and Suming is the same, we can form a ratio relationship between time taken and speed. The ratio in terms of time for Winnie and Suming will be 8 : 14, therefore the ratio in terms of speed for Winnie and Suming will be 14 : 8.

The second clue is “Winnie passed Suming 135 km away halfway between the 2 cities” Based on this clue, we can conclude that Winnie travelled 270 km more than Suming.

135 km x 2 = 270 km

The third clue is “They started driving at the same time”

Since the time taken is the same, we can form a ratio relationship between speed and distance travelled. As the ratio in terms of speed for Winnie and Suming is 14 : 8, we can conclude that the ratio in terms of distance travelled for Winnie and Suming is also 14 : 8

Based on this ratio, we can observe that the distance travelled by Winnie is 6 units more than Suming, we can further infer the following :

6 units = 270km

270km ÷ 6 = 45 km (1 unit)

The distance between both cities will be equal to the total distance travelled by Winnie and Suming

22 x 45 = 990 (22 units)

**ANS: 990 km**

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